# Water reservoir

The water reservoir is filled through one inlet 4 hours later than both together, then another inlet 9 hours later than both together. For how long is filled by each separately?

Correct result:

a =  10 h
b =  15 h

#### Solution:

$\dfrac1a + \dfrac1b = \dfrac1s \ \\ s = \dfrac{ab}{a+b} \ \\ a = 4 +s \ \\ b = 9 + s \ \\ \ \\ a = 4 + \dfrac{ab}{a+b} \ \\ b = 9 + \dfrac{ab}{a+b} \ \\ \ \\ a^2 = 4(a+b) \ \\ b^2 = 9(a+b) \ \\ \ \\ a>0; b>0 \ \\ a = 10 \ \\ b = 15 \ \\ s = 6 \ \\$

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